1193
Discussion
Papers
Deutsches Institut für Wirtschaftsforschung
Do Media Data Help to Predict
German Industrial Production?
Konstantin A. Kholodilin, Tobias Thomas and Dirk Ulbricht
2014
Opinions expressed in this paper are those of the author(s) and do not necessarily reflect views of the institute.
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Do media data help to predict German industrial production?
Konstantin A. Kholodilin∗
Tobias Thomas†
Dirk Ulbricht‡
June 25, 2014
Abstract
Expectations form the basis of economic decisions of market participants in an uncertain world. Sentiment indicators reflect those expectations and thus have a proven track record for predicting economic
variables. However, respondents of surveys perceive the world to a large extent with the help of media. So
far, mainly very crude media information, such as word-count indices, has been used in the prediction of
macroeconomic and financial variables. In this paper, we employ a rich data set provided by Media Tenor
International, based on the sentiment analysis of opinion-leading media in Germany from 2001 to 2014,
whose results are transformed into several monthly indices. German industrial production is predicted in a
real-time out-of-sample forecasting experiment using more than 17,000 models formed of all possible combinations with a maximum of 3 out of 48 macroeconomic, survey, and media indicators. It is demonstrated
that media data are indispensable when it comes to the prediction of German industrial production both
for individual models and as a part of combined forecasts. They increase reliability by improving accuracy
and reducing instability of the forecasts, particularly during the recent global financial crisis.
Keywords: forecast combination, media data, German industrial production, reliability index, R-word.
JEL classification: C10; C52; C53; E32.
∗ Research
associate, DIW Berlin, Mohrenstraße 58, 10117 Berlin, Germany, e-mail: kkholodilin@diw.de.
of research, Media Tenor International, Alte Jonastraße 48, 8640, Switzerland, and research affiliate, Düsseldorf
Institute for Competition Economics (DICE), Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, e-mail:
t.thomas@mediatenor.com.
‡ Research associate, DIW Berlin, Mohrenstraße 58, 10117 Berlin, Germany, e-mail:
dulbricht@diw.de.
† Head
I
Contents
1 Introduction
1
2 Empirical approach and data
3
2.1
Empirical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2.2
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
3 Forecast evaluation
8
3.1
Measures for comparing performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
3.2
Performance of individual models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
3.3
Performance of forecast combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Conclusion
14
References
15
Appendix
18
II
List of Tables
1
Macroeconomic indicators: definitions and descriptive statistics . . . . . . . . . . . . . . . . . . . 18
2
Analyzed Media Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3
Sentiment indicators: definitions and descriptive statistics . . . . . . . . . . . . . . . . . . . . . . 19
4
Media indicators: definitions and descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . 20
5
Best models: July 2001 to April 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6
Best models: May 2008 to January 2009, recession period . . . . . . . . . . . . . . . . . . . . . . 22
7
Combinations: July 2001 to April 2014, sorted by coefficient of reliability . . . . . . . . . . . . . 23
8
Combinations: May 2008 to January 2009, recession period, sorted by coefficient of reliability . . 24
List of Figures
1
Precision and stability over all periods: individual models versus combinations . . . . . . . . . . 25
2
Precision and stability during recession: individual models versus combinations . . . . . . . . . . 26
III
1
Introduction
Typically, the data on gross domestic product (GDP) are available on a quarterly basis. In addition, they are
published half a quarter after the end of the reference quarter. Therefore, in order to get a quick insight into
the current economic situation, a monthly series of industrial production is used. It is thus a central monthly
indicator for the business activity. This is especially the case for Germany. Although the share of industrial
production has been shrinking over the past decades, it remains at high levels compared to other OECD and
especially other EU member countries1 . Moreover, the secular decline of the share is expected to reverse in the
coming years. Among others, the European Commission stresses the importance of the contribution of industrial
competitiveness to the overall competitiveness performance of the EU and aspires raising the contribution of
industry to GDP to as much as 20% by 2020 Commission (2014). Moreover, it substantially contributes to the
business cycle dynamics.
Consequently, there have been many attempts to improve forecast accuracy of this variable 2 . Most of these
studies employ hard economic indicators such as interest rates, manufacturing orders, etc. There have also
been several studies using soft data such as business surveys like the ifo or ZEW indicator (see, for example,
Abberger and Wohlrabe, 2006 or Hüfner and Schröder, 2002). It was demonstrated that due to their forwardlooking nature they are well-suited for forecasting industrial production. The underlying idea of this approach
is to employ a measure of the intentions or the expectations of the managers or analysts, respectively. The
main advantages of these indicators are: their high frequency, timeliness, and that they are almost not subject
to revisions in comparison to many statistical indicators.
While in classical economics the homo oeconomicus is omniscient and decides independently, and decisions
lead to efficient outcomes at the market level, Keynes (1937) underlined the role of uncertainty concerning
decisions and behavior and the related (suboptimal) outcomes on the macro level just as von Hayek (1992)
pointed to the pretense of knowledge. Similarly, Simon (1957) as well as Kahneman and Tversky (1979) have
shown that in reality human behavior clearly deviates from the behavior predicted by standard economic models.
Due to their limited information processing capacity, individuals use subjective models for the perception of
1 According to the OECD Factbook 2011: Economic, Environmental and Social Statistics, in 2010, the percentage of total value
added in industry (including energy) was 24% in Germany, 19% in the EU, and 21% in the OECD countries.
2 See, for example, Kholodilin and Siliverstovs, 2006.
1
reality. If these models are shared because of common cultural background and experience, in accordance with
Denzau and North (1994) one can speak of shared mental models. In media societies, media reporting does
form relevant parts of those shared mental models not only because investors, consumers, politicians, and voters
receive lots of information via the media, but because additional information perceived directly is interpreted
on the basis of the frame determined by the media reporting. Therefore, what is on the agenda (“agenda
setting”) and what is not (“agenda cutting”) becomes highly relevant, as well as the way in which these things
are described in the media, such as with a positive, negative or neutral tone. Individuals decide and behave at
least in parts on what information they perceive through the media. This is also important in the context of
business surveys, as respondents interpret their own economic situation and build their expectations within the
frame set by the media.
A growing literature employs media data to explain economic sentiment. For instance, Goidel and Langley
(1995) as well as Doms and Morin (2004) show an impact of media reporting on consumer climate. For Nadeau
et al. (2000) and Soroka (2006) the assessment of the state of the economy depends at least in parts on the
media reporting.
The literature can be split into two main classes. The first one simply counts the number of times a single
word or a group of words, which can be associated with a certain event, occur in the media. The second strand
of literature captures content expressed in the media:
The most popular word-count indicator has been introduced by the weekly journal The Economist. It counts
how many articles in the Washington Post and the New York Times use the word “recession” in a quarter. For
Germany this concept has been adapted by the HypoVereinsbank basing the count on articles in the Frankfurter
Allgemeine Zeitung, Handelsblatt, and WirtschaftsWoche and was published until 2002. More recently it has
been revived by Grossarth-Maticek and Mayr (2008) who, however, do not consider the Great Recession period.
Doms and Morin (2004) count the number of articles in 30 American newspapers that contain 9 keywords or
expressions in the title or the first section of the article and use this statistic to forecast US private consumption.
Ammann et al. (2011) compute the number of mentionings of a lexicon of 236 words in the online archive of the
Handelsblatt with the aim of predicting yields of the German stock market index DAX. Bordino et al. (2011)
use the number of queries of listed companies in the US search engine Yahoo! as a predictor for stock market
2
volumes. Using the number of queries in the alternative search engine Google, Kholodilin et al. (2010) try to
improve forecasts of US private consumption.
Media indicators that are based on the sentiment expressed in media reports use both automated methods
and human analyst to evaluate the news. Bollen et al. (2011) employ the software OpinionFinder to analyze
Twitter tweeds with the aim of forecasting stock prices. To the same end, Tetlock (2007) evaluates the sentiment
of articles of the Wall Street Journal. Uhl (2010, 2011) uses sentiment data of newspaper and TV-news provided
by Media Tenor International to forecast US private consumption. Iselin and Siliverstovs (2013) use the R-word
index to forecast the growth rates of real GDP in Germany and Switzerland.
The first and until now the only attempt to use media indices to predict German industrial production
was undertaken by Grossarth-Maticek and Mayr (2008). They contrast the R-word index for Germany and a
Media Tenor International index to predict growth rates of industrial production and recession probabilities.
Our approach differs from their approach in several respects. First, we consider a more recent period including
the Great Recession. Second, we examine all possible combinations of a much wider set of indicators. Third,
we evaluate the usefulness of media indicators in forecast combinations. Fourth, unlike Grossarth-Maticek and
Mayr (2008) who use a single aggregate Media Tenor International business conditions index, we employ 18
more indicators that differ both in their time perspective (present, future, and climate) and their underlying
topic (fiscal policy, foreign exchange, labour market, etc.). Fifth, we employ monthly instead of quarterly data.
Sixth, we develop and apply a novel measure of reliability to assess the forecasts. Seventh, we employ real-time
series of the dependent variable.
This paper is structured as follows. The second section presents the empirical approach and the data used
in the analysis. In section three the forecasts are evaluated. The fourth section concludes.
2
2.1
Empirical approach and data
Empirical approach
Many existing studies concentrate on the comparison of single models including one different alternative indicator
at a time in a horse race with respect to average forecast accuracy of a benchmark model such as the simple
3
autoregressive model (AR). However, as Stock and Watson (2004) have demonstrated, single models are prone
to structural breaks and tend to be less reliable when compared to combinations of many different forecasts. To
address this issue, we suggest a novel approach. In a first step, we estimate the models including all possible
combinations of indicators varying from one to a given maximum number of exogenous variables.
In a second step, we construct combined forecasts as weighted averages of the individual models predictions.
The individual models are defined as
yt = α +
PX
+l0
βp yt−p +
p=l0
+li
K PX
X
γi,p xi,t−p + ut ,
(1)
i=1 p=li
where α, βp , and γi,p are parameters to estimate, yt are year-on-year growth rates of industrial production in
time period t (t = 1, ..., T ), xi,t is an indicator variable i in time period t, and ut is a disturbance term. The
total number of indicator variables is N . Each individual model can contain a subset of K indicators. We
let K vary between 0 and 3. The different number of minimum lags lq for each regressor, with q = 0, ..., N ,
used reflects the varying degree of data availability. For example, as the dependent variable is published with
a lag of 2 months, l0 = 3. The number is dictated both by data limitations (the sample is relatively short) and
computational intensity. The number of parameters of an individual model ranges from 2 to 50.
The total number of individual models can be computed as M =
N!
K!×(N −K)!
+ 1. Given that we employ
48 regressors and up to three regressors in one model, the maximum number of models is M = 17, 296. In
fact, the number of individual models in our case is slightly smaller, since we excluded some combinations of
regressors due to their extremely high mutual correlation (with a correlation coefficient more than or equal to
0.95). Likewise, a model containing short-term, long-term interest rates, and the spread between them was
dropped to avoid multicollinearity. In the end, we are left with 17,135 individual models. With 4 regressors
the number of models attains 194,580, whereas with 5 regressors it would reach 1,712,304. Our computational
capacities preclude the estimation of so many models.
The lag order, P , is identical for all regressors and is determined using the Bayesian Information Criterion
(BIC) with a maximum of 12.
In the simplest case, when N = 0 the model boils down to an autoregressive process, which we employ as a
benchmark model.
4
The whole sample stretches from January 2001 to April 2014. The data set is unbalanced: some series start
in March 2001. On the other hand, the publication delays are different, so the data are characterized by a
ragged edge. In order to address this problem, the series are shifted forward correspondingly.
We perform an out-of-sample forecast experiment. The first estimation sub-sample, TE , ends in June 2004.
The first forecast is performed for July 2004. The estimation and forecasting are implemented in a recursive
way. The forecast horizon is h = 1 month. Thus, the number of forecasts for each model is 112.
All the computations in this paper have been carried out using the codes written by the authors in the
statistical programming language R (see R Core Team, 2013).
2.2
Data
The dependent variable is the monthly series of real-time German industrial production, taken from the Deutsche
Bundesbank database (see Table 1).
The set of regressors includes 15 macroeconomic indicators, 11 purely business survey data and two composite
indicators3 , and 19 media indicators. Tables 1, 3, and 4 list the variables, their sources, and report some
descriptive statistics.
In this paper, two types of media indicators are considered: word-count indices and sentiment-analysis
indices.
The word-count indices are the simplest form of the media sentiment indicators. The idea is simple: one
counts the occurrences of a word or group of words, whose polarity can be determined more or less unambiguously, in several media. One example of such index is the famous recession index, or R-word index, of
The Economist. It counts the number of articles in the Washington Post and the New York Times using the
word “recession” in a quarter. In Germany, similar indicator had been developed at the HypoVereinsbank.
However, several years ago the publication of the index was given up. Therefore, we had to reconstruct it.
For this purpose we computed the number of articles published in the most influential German general and
economic newspapers (Frankfurter Allgemeine Zeitung, Handelsblatt, and Süddeutsche Zeitung) and in one
business journal (WirtschaftsWoche) containing the word “Rezession”. The counts for Frankfurter Allgemeine
3 The two OECD composite leading indicators for Germany are based on several components such as macroeconomic variables
(new orders, spread, etc.) and ifo business survey indicator.
5
Zeitung were obtained using the online archive search of the newspaper4 . To calculate the number of articles
in Handelsblatt and WirtschaftsWoche we used their joint article database5 . Finally, for Süddeutsche Zeitung
the word occurrences were recovered from the database Genios.6
The simple R-word index was constructed in a two-step procedure: First, the “Rezession” word occurrences
were aggregated to the monthly frequency by computing the monthly means. Secondly, the monthly series were
added up across the four media. However, since our sample includes both general and specialized media, we
have to account for their different exposure to the word “recession”: the relative frequency of the word varies
from 0.4% in Süddeutsche Zeitung to 2.4% in WirtschaftsWoche. Hence, the simple adding of the mediumspecific averages could introduce a bias. In order to address the problem we computed a scaled R-word index
by dividing the number of monthly occurrences of the word “Rezession” by those of the word “der” for each
medium. The latter word was chosen as a proxy for the overall text size, given that it is the most frequent word
in German language.
A more sophisticated way to analyze media is the method of content analysis. Content analysis “is a research
technique for the objective, systematic, and quantitative description of the manifest content of communication”
(Berelson (1952), 18). There exist many different types of content analysis, going beyond simple frequency counts
such as complicated assessments of arguments and media frames. Our contribution is based on the analysis
of the content of opinion-leading media in Germany, including five TV news programs, two weekly magazines,
and one daily tabloid newspaper by the Swiss-based media analysis institute Media Tenor International. News
items only referring to the state of the economy in the media set were analyzed over the period from January
1, 2001 through March 31, 2014. Hence, the data set analyzed can be seen as a subset of a much bigger data
set including news items on all possible protagonists, such as persons (politicians, entrepreneurs, managers,
celebrities, etc.) and institutions (political parties, companies, football clubs, etc.). Each of these news items
was analyzed with regard to the topic mentioned (unemployment, inflation, etc.), the region of reference (for
example, Germany, EU, USA, UK, BRIC, worldwide), the time reference (such as past, present, and future), the
source of information (journalist, politician, expert, etc.), as well as with regard to the tone of the information
(negative, positive or neutral).7 Overall 80,675 news items about the state of the economy have been analyzed.
4 www.faz.de
5 www.wirtschaftspresse.biz
6 www.genios.de
7 Media
Tenor International employs professional coders to carry out media-analysis. Only coders that achieved a minimum
6
For a detailed description of the analyzed media set see Table 2.
Table [Analyzed Media Set] about here
Based on the rating we computed Media Tenor International indices (MT) as the differences between the
percentage share of the positive ratings and the that of the negative ratings:
Bi,j,t = 100 ×
−
A+
i,j,t − Ai,j,t
−
0
A+
i,j,t + Ai,j,t + Ai,j,t
(2)
where A+
it is the number of positive ratings of medium reports about events happening in the time i in the
0
country j, published in the period t, A−
i,j,t is the number of negative ratings, and Ai,j,t is the number of neutral
ratings. The index varies between −100 (all reports are negatively rated) and 100 (all reports are positively
rated).
In this study, we construct four overall indices: media sentiments regarding all countries in the present, media
sentiments concerning all countries in the future, media sentiments regarding only Germany in the present, and
media sentiments concerning only Germany in the future. In addition, we compute similar indices for 5 most
frequent economic topics (budget, currency, labour market, business cycle, and taxation, see Table 4).
Moreover, the indices of the present and the future sentiment are employed to construct a so-called media
climate index:
q
M CI =
present
f uture
(M Sit
+ 100)(M Sit
+ 100)
(3)
present
f uture
where M Sit
is the present sentiment index and M Sit
is the future sentiment index. By construction,
the MCI can take values between 0 indicating extremely bad media climate and 200 pointing to an excellent
media climate.
reliability of 0.85 are cleared for coding. That means that the coding of these coders deviate at most by 0.15 from the trainers’
master-versions. The reliability of the coding is checked on an ongoing basis, both with quarterly standard tests and random spot
checks. For each month and coder, three analyzed reports are selected randomly and checked. Coders scoring lower than 0.80 are
removed from the coding process. In none of the months the mean deviation among all coders was above 0.15.
7
3
Forecast evaluation
3.1
Measures for comparing performance
Typically, the usefulness of a forecasting model is evaluated based on its precision. Here, the precision of the
models over all periods is measured by the Root Mean Squared Forecast Error (RMSFE) and the Theil’s U.
The RMSFE is calculated as
v
u T
u X
RM SF E = t
(ŷi,t − yt )2 ,
(4)
t=TE +1
where ŷm,t is the forecast made by model m (m = 1, ..., M ) for period t, t = TE + 1, ..., T, where TE is the first
estimation subsample and yt is the realized value. Here, the Theil’s U is constructed such that it compares the
forecast performance of model m to that of the benchmark AR-model. It is computed as ratio of the RMSFE
of model m and the RMSFE of the autoregressive model
T heilsUm =
RM SF Em
RM SF EAR
(5)
The RMSFE and Theil’s U are average measures over all periods and therefore do not reflect the instability of
performance of individual models over time. In fact, the rank of a model according to its accuracy can fluctuate
enormously: being the best model in some periods, in others it can rank the worst. Surely, huge instability is not
a desirable property of a forecasting model. In order to take this into account we need a new forecast performance
measure. Firstly, let us define a single-period rank of model m in period t as ρm,t = rank(RM SF Em,t ). Thus,
the model with the lowest RM SF E in period t obtains the rank of 1. Secondly, with an eye to the construction
of our third measure below, we want the rank to be independent of the number of models and negatively
correlated to the RM SF E. Therefore, we compute the transformed rank by calculating the percentage of all
models outperformed by model m in period t
ρm,t × 100.
ρ̃m,t = 1 −
M
Thirdly, we compute the average transformed rank for each model m over all periods
8
(6)
P ercOutm =
ΣTt=TE +1 ρ̃m,t
.
T − TE
(7)
This measure can be interpreted as the average percentage of models outperformed by model m over time.
It can vary between 0 and 100 per cent. The larger its value, the better the precision of the respective model.
It can be considered as a complement to RMSFE, although it can be expected that both are highly correlated.
Fourthly, the instability of model m in each period can be measured as the standard deviation of its respective
transformed rank over time, σρ̃ = sd(ρ̃m,t ). The larger its value, the more instable the forecasting performance
of a model over time. It is the average percentage point dispersion of ρ̃m,t around its mean, P ercOutm . Of two
models with the same P ercOutm we would prefer the one with the lower σρ̃ .
Finally, we construct a measure of reliability, which takes into account both precision and stability. A reliable
model is the model with a high precision and a low instability. Thus, we define the measure Rm as
Rm =
P ercOutm
.
σρ̃
(8)
Rm is an increasing function of the average relative precision with respect to the alternative models and a
decreasing function of its instability. In fact, it is an inverted coefficient of variation. It is analogous to the
Sharpe ratio in finance.
3.2
Performance of individual models
Table [Best models: July 2001 to April 2014, 5] about here
Table 5 compares the performance of the five best individual models, which is, without considering combined
forecasts, over all forecasting periods. Our analysis provide here allows for the comparison of media and nonmedia indicators. However, due to the differences in the underlying media set, R-word and Media Tenor
International based indicators are not comparable to each other.8 Columns I to III show the RMSFE and
Theil’s U as well as the ranking of each model according to the two measures, columns IV and V present the
mean percentage of models outperformed by the respective model and the corresponding rank. Columns VI
8 For
a description of the underlying media sets see section 2.2.
9
and VII show the standard deviation of the percentage of models outperformed by the respective model and
its ranking. Columns VIII and IX report the coefficient of reliability and the corresponding rank, and column
X and XI present its best and worst rank over all periods. Lines 1 through 5 show the five best models with
respect to RMSFE and Theils’ U, lines 6 through 10 the five best models with respect to the mean percentage
of models outperformed, lines 11 through 15 the five best models according to stability, and lines 16 through
20 the five best models with respect to reliability.
According to RMSFE, standard deviation of rank, and coeffcient of reliability, models using media data
clearly outperform models without media data. In particular, according to RMSFE, standard deviation of rank,
and coefficient of reliability, as well as the second best model with respect to the number of models outperformed
on average employs MT.currency, cli.ger, and manuf.order. Its Root Mean Forecast Error is 43% lower than
that of the benchmark AR model giving a Theil’s U of 57. On average it outperforms 69.8% of the alternative
individual models. The standard deviation of its rank is 21.84, however, it oscillates between a minimum of
99 and a maximum of 15859. This wide range of ranks is also observed for the other high performing models.
Its coefficient of reliability is 319.6. About 50% of German exports are directed to countries outside the Euro
area. For some important sectors, like machinery, investment goods, and cars more than 50% of the overall
production are exported. Thus, media information on currency issues such as provided by MT.currency is
crucial for predicting industrial production.9
Apart from MT.currency, two more Media Tenor International based indicators, namely MT.taxation with
its particular information on tax issues and MT.de, which consists all economy-related topics with an effect on
the German economy, form part of models ranking among the five best models in each category. The model
employing MT.taxation, cli.ger, and manuf.order ranks fifth with respect to the mean percentage of models
outperformed and 31st in terms of the standard deviation of this measure. In terms of the reliability indicator,
it ranks 6th. The model consisting of MT.de, esi.ger, and dax is the third best with respect to stability.
However, it only ranks 5081st according to RMSFE and 6254th according to the mean percentage of models
outperformed. Most of the media reports on taxes relate to taxes in general. Taxes increase budget constraints,
and so negatively affect demand for industrial production, for both companies and households. Hence, news
related to tax changes influence sales expectations, too.
9 Source:
German Federal Statistical Office.
10
Both R-word indicators form part of the the five best models. Together with R1 and manuf.order, rword
ranks fourth with respect to the standard deviation of the percentage of models outperformed and fifth according
to reliability. There is a striking contrast of its performance according to its mean forecast error and its mean
percentage of outperforming alternative models, ranking 820th regarding the former and 17th with respect to
the latter.
Table [Best models: May 2008 to January 2009, recession period, 6] about here
The period under consideration includes a so called “Great Recession”. To show which models are especially
good at predicting it, we separately analyze the recession period, which starts in May 2008 and ends in January
2009. It is based on the ECRI10 classical business cycle chronology.
Table 6 shows the corresponding results for the recession period only. When compared to the outcome over
all periods, the correlation of accuracy and reliability is lower for the recession period.
Again according to RMSFE, standard deviation of rank, and coefficient of reliability, models using media
data clearly outperform models without media data. In particular, according to RMSFE all five best models
contain media based indices such as MT indices as well as R-word. The number one model with respect to
RMSFE consists of both R-word and MT.taxation. Nevertheless, none of the models appears among the five
best models in more than one category. The improvement of accuracy when compared to the AR is higher than
when looking at the best models over all periods, the Theil’s U giving values between 43.4 and 43.7. However,
no model containing a media indicator ranges among the five best models, according to the mean percentage of
outperforming alternative models. The model containing MT.de.labor, trade.bal, and imp.pr is the third best
one according to the standard deviation of ranks. However, the most stable models are performing poorly with
respect to accuracy. Its rank with respect to RMSFE is 17,134 and with respect to the mean percentage of
models outperformed it is 17,135. Looking at reliability, four media indicators appear in the best models. The
model containing MT.de.cycle, dax, and usd is the best model with a value of 10.84, followed by the model
containing rword, cli.eur, and cons.conf has a value of 9.14, the model consisting of MT.all, zew, and esi.ger
ranks fourth with a value of 8.52, and MT.de in combination with zew and esi.ger ranks fifth with a value of
8.50. The standard deviations of ranks and their ranges are smaller when compared to the respective values
10 Economic
Cycle Research Institute, https://www.businesscycle.com.
11
of all periods. The standard deviation of the best model is 5.5, its minimum rank is 5729th and its maximum
rank is 8283th. With the exception of the second best model containing rword, which ranks 75th with respect
to RMSFE and 21th according to the mean percentage of models outperformed, the relative accuracy of the
best models is much lower when compared to the results over all periods. For RMSFE and the percentage of
models outperformed the best rank of the remaining 4 models is 4810 with a Theil’s U of 50.9, respectively 2936,
with a value of 83.7, both for the model containing R6, gfk, and dax. During the recession period, the media
information that directly addresses the overall situation of the economy, or those that reject it representing the
sentiment on all sectors such as MTI.all for all economies and MTI.de for the German economy are best suited
to predict industrial production.
3.3
Performance of forecast combinations
Table [Combinations: July 2001 to April 2014, sorted by coefficient of reliability, 7] about here
As shown, individual models are very instable over time. To illustrate the relationship of precision and
stability, we draw bivariate highest density regions plots11 in Figures 1 and 2 for the whole period and the
recession period, respectively. Each point in these graphs represents a single model. The horizontal axis shows
the percentage of models outperformed by the respective model. The vertical axis depicts the standard deviation
of the percentage of models outperformed by the respective model. The light-gray and yellow areas are bivariate
high density regions that cover 50 and 95% of the distribution, respectively. As Figure 1 shows, higher precision
of individual models is weakly positively correlated with stability. The best models are those with a high
precision and a high stability.
Following the literature, we try to improve upon this by evaluating the usefulness of media data in forecast
combinations of individual models. Indeed, as can be seen in Figures 1 and 2, the combination models improve
the relationship between precision and stability. They allow reducing substantially the instability without
incurring large losses in precision. Figure 1 presenting the results for all periods shows the dominance of the
combined forecasts with respect to stability. At the same time, they are among the most accurate forecasting
models. Figure 2 reports the results for the recession period. As the averages are based on fewer observations
11 See
Hyndman, 1996.
12
and due to the higher uncertainty over economic downturns, the bivariate highest density distribution is much
more spread in both dimensions. There is a group of models characterized by low accuracy and high stability. At
the same time there is a group of models having a higher accuracy but a very large instability. The advantages
of combinations are smaller but still pronounced. Higher precision of individual models can only be obtained
at the cost of increased instability.
Table 7 contrasts the results of the combined forecast of all models not containing media indices (benchmark,
in italics) with combinations that employ both all non-media and one media index at a time to see, whether
this improves the performance. The table is based on the results for all periods and the models are sorted by
the coefficient of reliability. The standard deviation of the combined forecasts is markedly lower than that of
the best individual models. The worst ranks of the combinations are much lower, as well. This results in the
combinations being the best models with respect to the coefficient of reliability.
As shown in the analysis of the individual models, concerning combinations again models using media data
clearly outperform models without media data. According to the coefficient of reliability the best combination
contains models including rword sc. Six more media indices improve the benchmark. In descending order with
respect to reliability these are MT.taxation, MT.de.taxation, rword, MT.de, MT.de.cycle, and MT.currency.
However, difference in the ranks in between the media-based models can determined by the difenrences in the
media set used.
The addition of models containing the remaining media indices leads to a deterioration with respect to
reliability when compared to the benchmark model. In general, the performance of the combined forecasts does
not display substantial differences.
Table [Combinations: May 2008 to January 2009, recession period, sorted by coefficient of reliability, 8] about
here
Table 8 reports the forecast performance of combined models for the recession period from May 2008 to
January 2009 only. Again, models using media data clearly outperform models without media data. The
combinations of models including R-word indicators rank first and second according to the reliability measure
followed by eleven other combinations including media indices, such as MT.cycle, MT.future, MT.climate, and
MT.all. These combinations are superior in terms of precision to the remaining combinations, in particular,
13
to the combination of all non-media models, which rank 14th. The media combination has on average a 4%
smaller forecast error than the combination of all non-media models. In comparison to the benchmark model,
the autoregressive model, the improvement is about 20%. The mean percentage of models outperformed by the
best media combination is by 3 percentage points higher than the combination of all non-media models. The
standard deviation of 7.28 is about 1.5 percentage points lower. Thus, the media models are both more accurate
and less instable resulting in a higher reliability measure. Interestingly, MT.all that is based on all news ranks
relatively high. This means, that the overall media sentiment can be useful in predicting recessions.
4
Conclusion
In this paper, we analyzed the usefulness of media indicators for the prediction of monthly series of German
industrial production growth. We used two types of media indicators: a simple word-count index of the word
“recession” and several Media Tenor International indices which are based on a more sophisticated method
using human analysts of reports in German opinion-leading media. The forecast performance was evaluated
through forecast experiment covering the period from July 2004 to April 2014. In addition, we consider the
period of the Great Recession using the business cycle chronology of ECRI, to see whether the media indices
improve recession forecasts. More than 17,000 individual models representing all possible combinations with a
maximum of 3 out of 48 macroeconomic, survey, and media indicators were employed.
The forecasting performance was evaluated using four different criteria. First, we use two measures of forecast
accuracy, namely the Root Mean Squared Forecast Error and the mean percentage of outperformed alternative
models each period. Then, as a measure of stability we employ the standard deviation of the percentage of
outperformed alternative models each period. Finally, we introduce and apply our own measure of reliability,
which aggregates the information on accuracy and stability.
The results clearly show, models using media data outperform models without media data. This is case
according to both individual models as well as combinations of the individual models.
Individual models using media data are among the best models with respect to accuracy and stability over
the whole sample period. For the overall sample, the Media Tenor International index based on news related
to foreign exchange market stands on top of the rankings in terms of all four criteria considered. This might
14
be due to the strong export-orientation of German industrial production. For the recession period, the models
including the R-word indices focusing on recessions by construction are particularly useful.
Combinations of the individual models improve the stability of the forecasts and lead to highly accurate
models at the same time. We tested if augmenting the combination of models not making use of media data
with models making use of one additional media index improves forecasts. Over the complete sample and the
recession period, some of the media augmented combinations lead to an improvement of forecast reliability. In
addition, media sentiment on the overall situation implicitly rejecting information on the business cycle improves
forecast combinations for the recession period.
Under the common heading of media data two very different groups of indicators have been employed. The
main differences is in the technique used to extract information from the media. Media Tenor International
extracts the overall sentiments from the media items with the help of specialized analysts, while R-word simply
counts occurrences of one word. However, the data sets employed here are not comparable: they are both nonoverlapping and cover different segments of media. Although these differences do not preclude the comparison
of their helpfulness in the prediction of industrial production, a deeper analysis is needed to understand the
impact of these differences on the forecasting performance. This is left to future research.
Nevertheless, our analysis have clearly shown that when it comes to the forecast of industrial production
models using media data clearly outperform models without media data.
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17
Appendix
Table 1: Macroeconomic indicators: definitions and descriptive statistics
Indicator
Description
Source
Transformation
Mean
Standard
deviation
dax
DAX, German stock
market index
Deutsche
Börse AG
year-on-year
change rates
5.05
25.52
eur.stox
Eurostoxx 50, European
stock market index
STOXX Ltd.
year-on-year
change rates
-1.54
21.44
long.rate
long-term government
Datastream
3.43
1.08
2.19
1.26
bond yields, 9-10 years
short.rate
short-term euro
repo rate
European Central
Bank
oil
crude Brent oil in
US dollar per barrel
Datastream
year-on-year
change rates
15.57
33.32
manuf.order
manufacturing
orders
German Federal
Statistical Office
year-on-year
change rates
2.44
11.35
usd
US dollar – euro
exchange rate
Datastream
year-on-year
change rates
3.29
9.90
ex
German exports of
goods and services
Deutsche
Bundesbank
year-on-year
change rates
5.26
9.57
year-on-year
4.60
10.72
13.13
2.82
im
German imports
Deutsche
goods and services
Bundesbank
trade.bal
German trade
balance
Deutsche
Bundesbank
ex.pr
German export
price inflation
Deutsche
Bundesbank
year-on-year
change rates
0.90
1.60
im.pr
German import
price inflation
Deutsche
Bundesbank
year-on-year
change rates
1.12
4.67
tot
terms of trade
Deutsche
Bundesbank
year-on-year
change rates
-0.07
3.25
infl
consumer price
inflation
German Federal
Statistical Office
1.62
0.68
authors’
1.22
0.71
1.82
7.31
spread
ip
long-term minus
and short-term rates
calculation
industrial production
Deutsche
Bundesbanka
a http://www.bundesbank.de/Navigation/DE/Statistiken/Suche
18
change rates
year-on-year
change rates
Statistik/Echtzeitdaten/statistiksuche rtd node.html
TV-Program / Newspaper
TV-newscasts:
ARD Tagesschau
ARD Tagesthemen
ZDF heute
ZDF heute journal
RTL Aktuell
Weekly magazines:
Spiegel
Focus
Daily newspaper:
Bild
Total
Table 2: Analyzed Media Set
Number of news items analysed
11,472
14,933
10,158
15,415
6,167
4,833
7,111
10,586
80,675
Table 3: Sentiment indicators: definitions and descriptive statistics
Indicator
R1
Description
Source
Transformation
Mean
Standard
deviation
102.36
7.63
business climate,
ifo Institute for
levels
Economic Research
R2
business situation,
levels
ifo Institute for
Economic Research
104.50
10.87
R3
business expectations,
levels
ifo Institute for
Economic Research
100.44
6.34
R4
business climate,
balances
ifo Institute for
Economic Research
-2.33
14.74
R5
business situation,
balances
ifo Institute for
Economic Research
-1.66
20.64
R6
business expectations,
balances
ifo Institute for
Economic Research
-2.61
12.44
17.40
35.05
zew
ZEW indicator
Centre for European
of economic sentiment
Economic Research
esi.eu
economic sentiment indicator,
European Union
European
Commission
99.15
9.43
esi.ger
economic sentiment
indicator, Germany
European
Commission
98.18
9.60
cli.eur
composite leading indicator,
Euro area (18 countries)
OECD
99.95
1.19
cli.ger
composite leading
indicator, Germany
OECD
99.98
1.48
cons.conf
confidence indicator
European
Commission
-7.94
9.66
gfk
GfK consumer index
Society for Consumer
4.86
3.88
Research
19
Table 4: Media indicators: definitions and descriptive statistics
Indicator
Description
Source
MT.all
all countries, assessment of
current situation and expectation
MT.future
MT.present
MT.climate
Transformation
Mean
Standard
deviation
Media Tenor
International
-29.89
16.04
all countries,
expectation
Media Tenor
International
-20.13
18.91
all countries, assessment of
current situation
Media Tenor
International
-35.14
16.96
71.58
16.26
all countries, Media Climate
Media Tenor
Index, see equation 3
International
MT.de
Germany, assessment of current
situation and expectation
Media Tenor
International
-20.85
19.07
MT.de.future
Germany,
expectation
Media Tenor
International
-14.41
18.94
MT.de.present
Germany, assessment of
current situation
Media Tenor
International
-24.92
22.27
MT.de.climate
Germany, Media Climate
Index, see equation 3
Media Tenor
International
79.57
18.62
MT.budget
all countries, assessment of current situation
and expectation, government budget
Media Tenor
International
-42.83
26.92
-26.77
34.24
MT.currency
all countries, assessment of current situation
Media Tenor
and expectation, currency related issues
International
MT.labor
all countries, assessment of current situation
and expectation, labor market related issues
Media Tenor
International
-28.06
19.74
MT.cycle
all countries, assessment of current situation
and expectation, business cycle related issue
Media Tenor
International
-22.37
35.43
MT.taxation
all countries, assessment of current situation
and expectation, taxation related issues
Media Tenor
International
-26.33
15.17
MT.de.budget
Germany, assessment of current situation
and expectation, government budget
Media Tenor
International
-29.07
33.48
MT.de.labor
Germany, assessment of current situation
and expectation, labor market related issues
Media Tenor
International
-23.35
22.00
-1.57
47.91
-26.67
15.61
MT.de.cycle
Germany, assessment of current situation
Media Tenor
and expectation, business cycle related issue
International
MT.de.taxation
Germany, assessment of current situation
and expectation, taxation related issues
Media Tenor
International
rword sc
recession word indicator scaled
by the overall number of words
authors’
calculation
9.37
8.00
rword
recession word indicator
authors’
calculation
13.93
12.46
20
MT.taxation, cli.ger, manuf.order
MT.currency, cli.ger, manuf.order
8
9
10
11
outperformed
each period
21
(P ercOut)
rword, R1, manuf.order
cli.ger, dax, manuf.order
MT.currency, cli.ger, manuf.order
14
15
16
Rank
cli.ger, dax, manuf.order
rword, R1, manuf.order
19
20
(Coef Rel)
cli.ger, manuf.order, im
18
of reliability
cli.ger, manuf.order, ex
17
Coefficient
MT.de, esi.ger, dax
13
deviation
rword sc, cli.ger, tot
12
Standard
cli.ger, dax, manuf.order
cli.ger, manuf.order, ex
MT.currency, cli.ger, manuf.order
7
of models
R5, manuf.order, infl
5
cli.ger, manuf.order, im
cli.ger, manuf.order, im
4
6
rword sc, esi.eu, manuf.order
cli.ger, dax, manuf.order
3
MT.currency, cli.ger, manuf.order
2
Variables included in the model
1
#
Line
Mean %
RMSFE
criterion
57.13
68.77
4.56
58.93
64.65
3.79
3.91
4.28
56.67
57.13
3.79
3.76
68.77
88.07
68.22
56.67
71.93
57.13
64.65
56.67
58.93
58.94
58.93
4.56
5.84
4.52
3.76
4.77
3.79
4.28
3.76
3.91
3.91
3.91
58.78
57.13
3.90
56.67
3.79
Theil’s U
Value
3.76
II
I
RMSFE
820
2
4
387
1
2
820
5081
762
1
1087
2
387
1
4
5
4
3
2
1
Rank
III
67.27
69.16
70.08
69.67
69.80
69.16
67.27
52.07
62.72
69.80
69.05
69.16
69.67
69.80
70.08
66.29
70.08
67.50
69.16
69.80
Value
IV
V
17
4
1
3
2
4
17
6254
692
2
5
4
3
2
1
58
1
13
4
2
Rank
22.28
22.29
22.56
22.33
21.84
22.29
22.28
22.25
21.91
21.84
22.98
22.29
22.33
21.84
22.56
26.50
22.56
25.38
22.29
21.84
Value
VI
4
5
15
7
1
5
4
3
2
1
31
5
7
1
15
3461
15
1282
5
1
Rank
VII
each period
(P ercOut)
of rank
each period
outperformed
Standard
deviation
Mean %
of models
Coefficient
3.02
3.10
3.11
3.12
3.20
3.10
3.02
2.34
2.86
3.20
3.00
3.10
3.12
3.20
3.11
2.50
3.11
2.66
3.10
3.20
Value
VIII
5
4
3
2
1
4
5
1124
17
1
6
4
2
1
3
394
3
92
4
1
Rank
IX
(Coef Rel)
of reliability
135
51
133
22
99
51
135
431
66
99
20
51
22
99
133
103
133
8
51
99
Rank
X
Best
17076
15831
16435
15900
15859
15831
17076
16049
15805
15859
16511
15831
15900
15859
16435
16635
16435
16505
15831
15859
Rank
XII
Worst
Table 5: Best models: July 2001 to April 2014
ip, manuf.order, ex, tot
ip, R2, usd, tot
8
9
10
11
outperformed
each period
(P ercOut)
22
ip, R2, gfk, oil
ip, R5, gfk, oil
ip, MT.de.cycle, dax, usd
14
15
16
Rank
ip, R5, usd, tot
deviation
ip, MT.all, zew, esi.ger
ip, MT.de, zew, esi.ger
19
20
(Coef Rel)
ip, R6, gfk, dax
18
of reliability
ip, rword, cli.eur, cons.conf
17
Coefficient
ip, MT.de.labor, trade.bal, im.pr
12
13
Standard
ip, manuf.order, tot, infl
ip, manuf.order, ex, infl
ip, manuf.order, ex, im.pr
7
of models
ip, rword, esi.ger, cli.eur
5
ip, manuf.order, im.pr, infl
ip, rword, MT.future, esi.eu
4
6
ip, rword, esi.eu, usd
ip, rword, MT.de.taxation, esi.eu
3
ip, rword, MT.taxation, esi.eu
2
Variables included in the model
1
#
Line
Mean %
RMSFE
criterion
43.44
2.09
4.15
4.11
3.60
2.45
3.94
6.51
6.51
6.91
6.57
6.57
2.46
2.36
86.05
85.41
74.77
50.94
81.83
135.06
135.07
143.50
136.44
136.45
51.05
48.89
48.76
51.38
2.48
2.35
47.60
43.72
43.72
43.60
2.29
2.11
2.11
2.10
43.59
Theil’s U
Value
2.10
II
I
RMSFE
8412
8234
4810
75
7126
17054
17055
17134
17085
17086
76
44
41
81
33
5
4
3
2
1
Rank
III
52.11
52.80
70.11
83.74
59.65
2.34
2.34
1.75
2.21
2.20
85.55
86.52
86.66
86.69
87.28
83.93
83.46
84.73
83.79
84.13
Value
IV
V
8685
8412
2936
21
6072
17122
17123
17135
17129
17130
5
4
3
2
1
16
35
9
19
13
Rank
6.13
6.20
7.78
9.16
5.50
2.41
2.40
2.14
2.07
2.06
16.76
20.35
21.54
14.75
15.58
20.55
31.62
30.85
30.86
30.94
Value
VI
98
101
201
312
81
5
4
3
2
1
3247
6219
7397
2012
2500
6428
16554
16313
16318
16351
Rank
VII
each period
(P ercOut)
of rank
each period
outperformed
Standard
deviation
Mean %
of models
Coefficient
8.50
8.52
9.02
9.14
10.84
0.97
0.97
0.81
1.06
1.06
5.11
4.25
4.02
5.88
5.60
4.08
2.64
2.75
2.71
2.72
Value
VIII
5
4
3
2
1
15871
15854
16517
15450
15451
251
657
852
86
133
803
5749
4914
5134
5102
Rank
IX
(Coef Rel)
of reliability
5960
5821
3031
61
5729
16145
16165
16027
16092
16094
1
26
140
4
26
1
127
51
40
48
Rank
X
Best
9415
9417
7230
5597
8283
17107
17106
17130
17135
17134
7014
9653
11434
5935
7625
11659
16937
16592
16696
16682
Rank
XII
Worst
Table 6: Best models: May 2008 to January 2009, recession period
Line
23
11
12
13
14
15
16
17
18
19
20
Combination including MT.future
Combination including MT.de.budget
Combination including MT.all
Combination including MT.labor
Combination including MT.climate
Combination including MT.de.present
Combination including MT.de.climate
Combination including MT.present
Combination including MT.de.labor
Combination including MT.budget
4.93
8
Combination of non-media data
9
7
Combination including MT.currency
10
6
Combination including MT.de.cycle
Combination including MT.cycle
5
Combination including MT.de
Combination including MT.de.future
4.91
4
Combination including rword
4.95
4.95
4.94
4.94
4.95
4.94
4.95
4.94
4.95
4.94
4.94
74.69
74.66
74.59
74.58
74.64
74.54
74.67
74.56
74.63
74.55
74.57
74.42
74.12
74.62
74.42
4.93
4.95
77.56
73.82
5.14
4.89
74.53
4.94
3
Combination including MT.de.taxation
74.52
73.98
4.94
4.90
1
Theil’s U
Value
2
II
RMSE
I
Combination including MT.taxation
#
Combination including rword sc
Variables included in the model
1358
1354
1344
1337
1351
1331
1356
1334
1350
1332
1335
1321
1291
1349
1320
1680
1247
1330
1329
1268
Rank
III
64.96
65.02
65.14
65.21
65.14
65.13
64.97
65.13
65.07
65.22
65.24
65.48
65.44
65.19
65.31
63.10
66.19
65.29
65.38
65.81
Value
IV
V
184
179
166
154
164
167
183
168
172
153
151
116
124
157
139
599
64
143
128
92
Rank
15.01
15.00
15.02
15.03
15.00
14.97
14.91
14.95
14.92
14.93
14.92
14.95
14.93
14.84
14.82
14.30
14.93
14.64
14.65
14.66
Value
VI
18
16
19
20
17
15
7
14
9
12
8
13
11
6
5
1
10
2
3
4
Rank
VII
each period
(P ercOut)
of rank
each period
outperformed
Standard
deviation
Mean %
of models
Coefficient
4.33
4.34
4.34
4.34
4.34
4.35
4.36
4.36
4.36
4.37
4.37
4.38
4.38
4.39
4.41
4.41
4.43
4.46
4.46
4.49
Value
VIII
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Rank
IX
(Coef Rel)
of reliability
16
21
90
114
130
108
24
29
22
341
66
1
240
12
226
272
17
7
81
75
Rank
X
Best
11642
11735
11708
11681
11737
11702
11664
11605
11559
11732
11728
11479
11788
11743
11470
10945
11496
11906
11778
11603
Rank
XII
Worst
Table 7: Combinations: July 2001 to April 2014, sorted by coefficient of reliability
Line
24
13
14
Combination including MT.currency
Combination of non-media data
20
12
Combination including MT.de.budget
Combination including MT.de.labor
11
Combination including MT.de.taxation
19
10
Combination including MT.taxation
Combination including MT.de
9
Combination including MT.present
18
8
Combination including MT.de.climate
Combination including MT.de.cycle
7
Combination including MT.de.future
17
6
Combination including MT.all
Combination including MT.budget
5
Combination including MT.climate
15
4
Combination including MT.future
16
3
Combination including MT.cycle
Combination including MT.de.present
2
Combination including MT.labor
1
Combination including rword sc
#
Combination including rword
Variables included in the model
4.10
4.18
4.07
4.09
4.10
4.08
4.06
4.09
4.09
4.08
4.08
4.08
4.08
85.21
86.89
84.51
85.01
85.19
84.80
84.40
84.96
84.86
84.62
84.66
84.65
84.70
84.68
84.59
4.08
4.08
84.62
4.08
84.63
84.34
4.06
4.08
82.65
3.98
80.63
Theil’s U
Value
3.88
II
I
RMSE
8195
8729
7952
8117
8191
8055
7920
8105
8072
7987
8004
8001
8020
8013
7980
7986
7990
7890
7368
6688
Rank
III
53.20
51.32
54.21
53.51
53.28
53.98
54.32
53.45
53.76
53.88
53.89
54.12
53.94
53.95
54.19
54.09
54.06
54.46
55.85
57.36
Value
IV
V
8266
8981
7848
8141
8238
7944
7800
8170
8029
7989
7985
7880
7963
7959
7853
7890
7901
7744
7204
6709
Rank
8.98
8.50
8.97
8.82
8.68
8.77
8.82
8.66
8.69
8.65
8.61
8.54
8.50
8.37
8.39
8.36
8.22
8.23
7.11
7.28
Value
VI
306
253
304
288
273
283
287
271
275
270
267
260
256
238
242
237
231
233
158
175
Rank
VII
each period
(P ercOut)
of rank
each period
outperformed
Standard
deviation
Mean %
of models
Coefficient
5.92
6.04
6.04
6.07
6.14
6.16
6.16
6.17
6.18
6.23
6.26
6.33
6.34
6.45
6.46
6.47
6.57
6.62
7.86
7.87
Value
VIII
96
85
84
82
71
68
66
63
61
56
51
46
44
39
38
37
34
32
9
8
Rank
IX
(Coef Rel)
of reliability
4677
4794
4748
4784
4767
4805
4823
4990
4844
4765
4778
4899
4926
5011
4955
4994
5071
5086
5978
5619
Rank
X
Best
10214
9966
10246
10300
10147
10294
10297
10337
10308
10173
10161
10240
10223
10204
10208
10210
10182
10143
9643
9144
Rank
XII
Worst
Table 8: Combinations: May 2008 to January 2009, recession period, sorted by coefficient of reliability
Figure 1: Precision and stability over all periods: individual models versus combinations
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Percentage of outperformed models
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Figure 2: Precision and stability during recession: individual models versus combinations
Combinations
Individual models
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10
20
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0
Standard deviation of percentage of outperformed models
●
0
20
40
60
Percentage of outperformed models
26
80
100